令X和Y是局部緊緻豪斯多夫空間。一個從C0(X,E)到C0(Y,F)的線性算子T，如果它能保持函數cozero的互斥性則它會被稱做保持互斥性算子。我們在本篇論文中研究一些保持互斥性算子的特例，證明了如果λ非零而且屬於σ(T)那麼λ
會是T的特徵值。我們找到一個投影算子，如果令Y1 = C0(X,E)和Y2 = (1-Π)C0(X,E)，我們證明了T-λ在Y1上會是幂零，T-λ在Y2上會是可逆的。

Let X, Y be locally compact Hausdorff spaces. A linear operator T from C0(X,E) to C0(Y,F) is called disjointness preserving if coz(Tf)∩coz(Tg) = whenever coz(f)∩coz(g) = ∅. We discuss some cases on these compact disjointness preserving operators T and prove that if λ0 is a nonzero point of σ(T), then λ0 is an eigenvalue of T and
we find a projection ∏: C0(X,E) →C0(X,E), such that for Y1 = ∏C0(X;E) and Y2 = (1-∏)C0(X;E), the operator T|Y1 -λ0 is a nilpotent and λ0-T|Y2 is invertible.

Chapter 1: Introduction 1
Chapter 2: Preliminary 3
Chapter 3: Main results 6
3.1 The case of one point cycle . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 The case of two points cycle . . . . . . . . . . . . . . . . . . . . . . . . 17
Bibliography 30

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